Kui Yu

Jianli Huang, Xianjie Guo, Kui Yu et al.

Causal structure learning has been extensively studied and widely used in machine learning and various applications. To achieve an ideal performance, existing causal structure learning algorithms often need to centralize a large amount of data from multiple data sources. However, in the privacy-preserving setting, it is impossible to centralize data from all sources and put them together as a single dataset. To preserve data privacy, federated learning as a new learning paradigm has attracted much attention in machine learning in recent years. In this paper, we study a privacy-aware causal structure learning problem in the federated setting and propose a novel Federated PC (FedPC) algorithm with two new strategies for preserving data privacy without centralizing data. Specifically, we first propose a novel layer-wise aggregation strategy for a seamless adaptation of the PC algorithm into the federated learning paradigm for federated skeleton learning, then we design an effective strategy for learning consistent separation sets for federated edge orientation. The extensive experiments validate that FedPC is effective for causal structure learning in a federated learning setting.

Ziqi Xu, Debo Cheng, Jiuyong Li et al.

An essential and challenging problem in causal inference is causal effect estimation from observational data. The problem becomes more difficult with the presence of unobserved confounding variables. The front-door adjustment is a practical approach for dealing with unobserved confounding variables. However, the restriction for the standard front-door adjustment is difficult to satisfy in practice. In this paper, we relax some of the restrictions by proposing the concept of conditional front-door (CFD) adjustment and develop the theorem that guarantees the causal effect identifiability of CFD adjustment. Furthermore, as it is often impossible for a CFD variable to be given in practice, it is desirable to learn it from data. By leveraging the ability of deep generative models, we propose CFDiVAE to learn the representation of the CFD adjustment variable directly from data with the identifiable Variational AutoEncoder and formally prove the model identifiability. Extensive experiments on synthetic datasets validate the effectiveness of CFDiVAE and its superiority over existing methods. The experiments also show that the performance of CFDiVAE is less sensitive to the causal strength of unobserved confounding variables. We further apply CFDiVAE to a real-world dataset to demonstrate its potential application.

Debo Cheng, Jiuyong Li, Lin Liu et al.

Instrumental variable (IV) is a powerful approach to inferring the causal effect of a treatment on an outcome of interest from observational data even when there exist latent confounders between the treatment and the outcome. However, existing IV methods require that an IV is selected and justified with domain knowledge. An invalid IV may lead to biased estimates. Hence, discovering a valid IV is critical to the applications of IV methods. In this paper, we study and design a data-driven algorithm to discover valid IVs from data under mild assumptions. We develop the theory based on partial ancestral graphs (PAGs) to support the search for a set of candidate Ancestral IVs (AIVs), and for each possible AIV, the identification of its conditioning set. Based on the theory, we propose a data-driven algorithm to discover a pair of IVs from data. The experiments on synthetic and real-world datasets show that the developed IV discovery algorithm estimates accurate estimates of causal effects in comparison with the state-of-the-art IV based causal effect estimators.

Yuling Li, Kui Yu, Yuhong Zhang et al.

Recent years have witnessed increasing interest in few-shot knowledge graph completion (FKGC), which aims to infer unseen query triples for a few-shot relation using a few reference triples about the relation. The primary focus of existing FKGC methods lies in learning relation representations that can reflect the common information shared by the query and reference triples. To this end, these methods learn entity-pair representations from the direct neighbors of head and tail entities, and then aggregate the representations of reference entity pairs. However, the entity-pair representations learned only from direct neighbors may have low expressiveness when the involved entities have sparse direct neighbors or share a common local neighborhood with other entities. Moreover, merely modeling the semantic information of head and tail entities is insufficient to accurately infer their relational information especially when they have multiple relations. To address these issues, we propose a Relation-Specific Context Learning (RSCL) framework, which exploits graph contexts of triples to learn global and local relation-specific representations for few-shot relations. Specifically, we first extract graph contexts for each triple, which can provide long-term entity-relation dependencies. To encode the extracted graph contexts, we then present a hierarchical attention network to capture contextualized information of triples and highlight valuable local neighborhood information of entities. Finally, we design a hybrid attention aggregator to evaluate the likelihood of the query triples at the global and local levels. Experimental results on two public datasets demonstrate that RSCL outperforms state-of-the-art FKGC methods.

Ziqi Xu, Debo Cheng, Jiuyong Li et al.

An essential problem in causal inference is estimating causal effects from observational data. The problem becomes more challenging with the presence of unobserved confounders. When there are unobserved confounders, the commonly used back-door adjustment is not applicable. Although the instrumental variable (IV) methods can deal with unobserved confounders, they all assume that the treatment directly affects the outcome, and there is no mediator between the treatment and the outcome. This paper aims to use the front-door criterion to address the challenging problem with the presence of unobserved confounders and mediators. In practice, it is often difficult to identify the set of variables used for front-door adjustment from data. By leveraging the ability of deep generative models in representation learning, we propose FDVAE to learn the representation of a Front-Door adjustment set with a Variational AutoEncoder, instead of trying to search for a set of variables for front-door adjustment. Extensive experiments on synthetic datasets validate the effectiveness of FDVAE and its superiority over existing methods. The experiments also show that the performance of FDVAE is not sensitive to the causal strength of unobserved confounders and is feasible in the case of dimensionality mismatch between learned representations and the ground truth. We further apply the method to three real-world datasets to demonstrate its potential applications.

Jiuyong Li, Ha Xuan Tran, Thuc Duy Le et al.

This paper studies the problem of estimating the contributions of features to the prediction of a specific instance by a machine learning model and the overall contribution of a feature to the model. The causal effect of a feature (variable) on the predicted outcome reflects the contribution of the feature to a prediction very well. A challenge is that most existing causal effects cannot be estimated from data without a known causal graph. In this paper, we define an explanatory causal effect based on a hypothetical ideal experiment. The definition brings several benefits to model agnostic explanations. First, explanations are transparent and have causal meanings. Second, the explanatory causal effect estimation can be data driven. Third, the causal effects provide both a local explanation for a specific prediction and a global explanation showing the overall importance of a feature in a predictive model. We further propose a method using individual and combined variables based on explanatory causal effects for explanations. We show the definition and the method work with experiments on some real-world data sets.

Zhaolong Ling, Enqi Xu, Peng Zhou et al.

Fair feature selection for classification decision tasks has recently garnered significant attention from researchers. However, existing fair feature selection algorithms fall short of providing a full explanation of the causal relationship between features and sensitive attributes, potentially impacting the accuracy of fair feature identification. To address this issue, we propose a Fair Causal Feature Selection algorithm, called FairCFS. Specifically, FairCFS constructs a localized causal graph that identifies the Markov blankets of class and sensitive variables, to block the transmission of sensitive information for selecting fair causal features. Extensive experiments on seven public real-world datasets validate that FairCFS has comparable accuracy compared to eight state-of-the-art feature selection algorithms, while presenting more superior fairness.

Libing Yuan, Shuaibo Hu, Kui Yu et al.

The widespread application of pre-trained language models (PLMs) in natural language processing (NLP) has led to increasing concerns about their explainability. Selective rationalization is a self-explanatory framework that selects human-intelligible input subsets as rationales for predictions. Recent studies have shown that applying existing rationalization frameworks to PLMs will result in severe degeneration and failure problems, producing sub-optimal or meaningless rationales. Such failures severely damage trust in rationalization methods and constrain the application of rationalization techniques on PLMs. In this paper, we find that the homogeneity of tokens in the sentences produced by PLMs is the primary contributor to these problems. To address these challenges, we propose a method named Pre-trained Language Model's Rationalization (PLMR), which splits PLMs into a generator and a predictor to deal with NLP tasks while providing interpretable rationales. The generator in PLMR also alleviates homogeneity by pruning irrelevant tokens, while the predictor uses full-text information to standardize predictions. Experiments conducted on two widely used datasets across multiple PLMs demonstrate the effectiveness of the proposed method PLMR in addressing the challenge of applying selective rationalization to PLMs. Codes: https://github.com/ylb777/PLMR.

Zhaolong Ling, Kui Yu, Yiwen Zhang et al.

Causal Learner is a toolbox for learning causal structure and Markov blanket (MB) from data. It integrates functions for generating simulated Bayesian network data, a set of state-of-the-art global causal structure learning algorithms, a set of state-of-the-art local causal structure learning algorithms, a set of state-of-the-art MB learning algorithms, and functions for evaluating algorithms. The data generation part of Causal Learner is written in R, and the rest of Causal Learner is written in MATLAB. Causal Learner aims to provide researchers and practitioners with an open-source platform for causal learning from data and for the development and evaluation of new causal learning algorithms. The Causal Learner project is available at http://bigdata.ahu.edu.cn/causal-learner.

Kui Yu, Xianjie Guo, Lin Liu et al.

Feature selection is a crucial preprocessing step in data analytics and machine learning. Classical feature selection algorithms select features based on the correlations between predictive features and the class variable and do not attempt to capture causal relationships between them. It has been shown that the knowledge about the causal relationships between features and the class variable has potential benefits for building interpretable and robust prediction models, since causal relationships imply the underlying mechanism of a system. Consequently, causality-based feature selection has gradually attracted greater attentions and many algorithms have been proposed. In this paper, we present a comprehensive review of recent advances in causality-based feature selection. To facilitate the development of new algorithms in the research area and make it easy for the comparisons between new methods and existing ones, we develop the first open-source package, called CausalFS, which consists of most of the representative causality-based feature selection algorithms (available at https://github.com/kuiy/CausalFS). Using CausalFS, we conduct extensive experiments to compare the representative algorithms with both synthetic and real-world data sets. Finally, we discuss some challenging problems to be tackled in future causality-based feature selection research.

Kui Yu, Jiuyong Li, Lin Liu

Causal discovery studies the problem of mining causal relationships between variables from data, which is of primary interest in science. During the past decades, significant amount of progresses have been made toward this fundamental data mining paradigm. Recent years, as the availability of abundant large-sized and complex observational data, the constrain-based approaches have gradually attracted a lot of interest and have been widely applied to many diverse real-world problems due to the fast running speed and easy generalizing to the problem of causal insufficiency. In this paper, we aim to review the constraint-based causal discovery algorithms. Firstly, we discuss the learning paradigm of the constraint-based approaches. Secondly and primarily, the state-of-the-art constraint-based casual inference algorithms are surveyed with the detailed analysis. Thirdly, several related open-source software packages and benchmark data repositories are briefly summarized. As a conclusion, some open problems in constraint-based causal discovery are outlined for future research.

Kui Yu, Wei Ding, Xindong Wu

As an emerging research direction, online streaming feature selection deals with sequentially added dimensions in a feature space while the number of data instances is fixed. Online streaming feature selection provides a new, complementary algorithmic methodology to enrich online feature selection, especially targets to high dimensionality in big data analytics. This paper introduces the first comprehensive open-source library for use in MATLAB that implements the state-of-the-art algorithms of online streaming feature selection. The library is designed to facilitate the development of new algorithms in this exciting research direction and make comparisons between the new methods and existing ones available.

Yukun Song, Dayuan Cao, Jiali Miao et al.

Multi-label feature selection serves as an effective mean for dealing with high-dimensional multi-label data. To achieve satisfactory performance, existing methods for multi-label feature selection often require the centralization of substantial data from multiple sources. However, in Federated setting, centralizing data from all sources and merging them into a single dataset is not feasible. To tackle this issue, in this paper, we study a challenging problem of causal multi-label feature selection in federated setting and propose a Federated Causal Multi-label Feature Selection (FedCMFS) algorithm with three novel subroutines. Specifically, FedCMFS first uses the FedCFL subroutine that considers the correlations among label-label, label-feature, and feature-feature to learn the relevant features (candidate parents and children) of each class label while preserving data privacy without centralizing data. Second, FedCMFS employs the FedCFR subroutine to selectively recover the missed true relevant features. Finally, FedCMFS utilizes the FedCFC subroutine to remove false relevant features. The extensive experiments on 8 datasets have shown that FedCMFS is effect for causal multi-label feature selection in federated setting.

Debo Cheng, Ziqi Xu, Jiuyong Li et al.

Intervention intuition is often used in model explanation where the intervention effect of a feature on the outcome is quantified by the difference of a model prediction when the feature value is changed from the current value to the baseline value. Such a model intervention effect of a feature is inherently association. In this paper, we will study the conditions when an intuitive model intervention effect has a causal interpretation, i.e., when it indicates whether a feature is a direct cause of the outcome. This work links the model intervention effect to the causal interpretation of a model. Such an interpretation capability is important since it indicates whether a machine learning model is trustworthy to domain experts. The conditions also reveal the limitations of using a model intervention effect for causal interpretation in an environment with unobserved features. Experiments on semi-synthetic datasets have been conducted to validate theorems and show the potential for using the model intervention effect for model interpretation.

Kui Yu, Zhaolong Ling, Lin Liu et al.

Local-to-global learning approach plays an essential role in Bayesian network (BN) structure learning. Existing local-to-global learning algorithms first construct the skeleton of a DAG (directed acyclic graph) by learning the MB (Markov blanket) or PC (parents and children) of each variable in a data set, then orient edges in the skeleton. However, existing MB or PC learning methods are often computationally expensive especially with a large-sized BN, resulting in inefficient local-to-global learning algorithms. To tackle the problem, in this paper, we develop an efficient local-to-global learning approach using feature selection. Specifically, we first analyze the rationale of the well-known Minimum-Redundancy and Maximum-Relevance (MRMR) feature selection approach for learning a PC set of a variable. Based on the analysis, we propose an efficient F2SL (feature selection-based structure learning) approach to local-to-global BN structure learning. The F2SL approach first employs the MRMR approach to learn a DAG skeleton, then orients edges in the skeleton. Employing independence tests or score functions for orienting edges, we instantiate the F2SL approach into two new algorithms, F2SL-c (using independence tests) and F2SL-s (using score functions). Compared to the state-of-the-art local-to-global BN learning algorithms, the experiments validated that the proposed algorithms in this paper are more efficient and provide competitive structure learning quality than the compared algorithms.

Zhaolong Ling, Kui Yu, Hao Wang et al.

We study an interesting and challenging problem, learning any part of a Bayesian network (BN) structure. In this challenge, it will be computationally inefficient using existing global BN structure learning algorithms to find an entire BN structure to achieve the part of a BN structure in which we are interested. And local BN structure learning algorithms encounter the false edge orientation problem when they are directly used to tackle this challenging problem. In this paper, we first present a new concept of Expand-Backtracking to explain why local BN structure learning methods have the false edge orientation problem, then propose APSL, an efficient and accurate Any Part of BN Structure Learning algorithm. Specifically, APSL divides the V-structures in a Markov blanket (MB) into two types: collider V-structure and non-collider V-structure, then it starts from a node of interest and recursively finds both collider V-structures and non-collider V-structures in the found MBs, until the part of a BN structure in which we are interested are oriented. To improve the efficiency of APSL, we further design the APSL-FS algorithm using Feature Selection, APSL-FS. Using six benchmark BNs, the extensive experiments have validated the efficiency and accuracy of our methods.

Xiang Wang, Xiaoyong Li, Junxing Zhu et al.

Real-world data usually have high dimensionality and it is important to mitigate the curse of dimensionality. High-dimensional data are usually in a coherent structure and make the data in relatively small true degrees of freedom. There are global and local dimensionality reduction methods to alleviate the problem. Most of existing methods for local dimensionality reduction obtain an embedding with the eigenvalue or singular value decomposition, where the computational complexities are very high for a large amount of data. Here we propose a novel local nonlinear approach named Vec2vec for general purpose dimensionality reduction, which generalizes recent advancements in embedding representation learning of words to dimensionality reduction of matrices. It obtains the nonlinear embedding using a neural network with only one hidden layer to reduce the computational complexity. To train the neural network, we build the neighborhood similarity graph of a matrix and define the context of data points by exploiting the random walk properties. Experiments demenstrate that Vec2vec is more efficient than several state-of-the-art local dimensionality reduction methods in a large number of high-dimensional data. Extensive experiments of data classification and clustering on eight real datasets show that Vec2vec is better than several classical dimensionality reduction methods in the statistical hypothesis test, and it is competitive with recently developed state-of-the-art UMAP.

Shuai Yang, Hao Wang, Kui Yu et al.

Local causal structure learning aims to discover and distinguish direct causes (parents) and direct effects (children) of a variable of interest from data. While emerging successes have been made, existing methods need to search a large space to distinguish direct causes from direct effects of a target variable T. To tackle this issue, we propose a novel Efficient Local Causal Structure learning algorithm, named ELCS. Specifically, we first propose the concept of N-structures, then design an efficient Markov Blanket (MB) discovery subroutine to integrate MB learning with N-structures to learn the MB of T and simultaneously distinguish direct causes from direct effects of T. With the proposed MB subroutine, ELCS starts from the target variable, sequentially finds MBs of variables connected to the target variable and simultaneously constructs local causal structures over MBs until the direct causes and direct effects of the target variable have been distinguished. Using eight Bayesian networks the extensive experiments have validated that ELCS achieves better accuracy and efficiency than the state-of-the-art algorithms.

Debo Cheng, Jiuyong Li, Lin Liu et al.

Causal effect estimation from observational data is a crucial but challenging task. Currently, only a limited number of data-driven causal effect estimation methods are available. These methods either provide only a bound estimation of the causal effect of a treatment on the outcome, or generate a unique estimation of the causal effect, but making strong assumptions on data and having low efficiency. In this paper, we identify a practical problem setting and propose an approach to achieving unique and unbiased estimation of causal effects from data with hidden variables. For the approach, we have developed the theorems to support the discovery of the proper covariate sets for confounding adjustment (adjustment sets). Based on the theorems, two algorithms are proposed for finding the proper adjustment sets from data with hidden variables to obtain unbiased and unique causal effect estimation. Experiments with synthetic datasets generated using five benchmark Bayesian networks and four real-world datasets have demonstrated the efficiency and effectiveness of the proposed algorithms, indicating the practicability of the identified problem setting and the potential of the proposed approach in real-world applications.

Debo Cheng, Jiuyong Li, Lin Liu et al.

This paper discusses the problem of causal query in observational data with hidden variables, with the aim of seeking the change of an outcome when "manipulating" a variable while given a set of plausible confounding variables which affect the manipulated variable and the outcome. Such an "experiment on data" to estimate the causal effect of the manipulated variable is useful for validating an experiment design using historical data or for exploring confounders when studying a new relationship. However, existing data-driven methods for causal effect estimation face some major challenges, including poor scalability with high dimensional data, low estimation accuracy due to heuristics used by the global causal structure learning algorithms, and the assumption of causal sufficiency when hidden variables are inevitable in data. In this paper, we develop a theorem for using local search to find a superset of the adjustment (or confounding) variables for causal effect estimation from observational data under a realistic pretreatment assumption. The theorem ensures that the unbiased estimate of causal effect is included in the set of causal effects estimated by the superset of adjustment variables. Based on the developed theorem, we propose a data-driven algorithm for causal query. Experiments show that the proposed algorithm is faster and produces better causal effect estimation than an existing data-driven causal effect estimation method with hidden variables. The causal effects estimated by the proposed algorithm are as accurate as those by the state-of-the-art methods using domain knowledge.

Shuai Yang, Hao Wang, Kui Yu et al.

Local causal structure learning aims to discover and distinguish direct causes (parents) and direct effects (children) of a variable of interest from data. While emerging successes have been made, existing methods need to search a large space to distinguish direct causes from direct effects of a target variable \emph{T}. To tackle this issue, we propose a novel Efficient Local Causal Structure learning algorithm, named ELCS. Specifically, we first propose the concept of N-structures, then design an efficient Markov Blanket (MB) discovery subroutine to integrate MB learning with N-structures to learn the MB of \emph{T} and simultaneously distinguish direct causes from direct effects of \emph{T}. With the proposed MB subroutine, ELCS starts from the target variable, sequentially finds MBs of variables connected to the target variable and simultaneously constructs local causal structures over MBs until the direct causes and direct effects of the target variable have been distinguished. Using eight Bayesian networks the extensive experiments have validated that ELCS achieves better accuracy and efficiency than the state-of-the-art algorithms.

Kui Yu, Lin Liu, Jiuyong Li

In this paper, we aim to develop a unified view of causal and non-causal feature selection methods. The unified view will fill in the gap in the research of the relation between the two types of methods. Based on the Bayesian network framework and information theory, we first show that causal and non-causal feature selection methods share the same objective. That is to find the Markov blanket of a class attribute, the theoretically optimal feature set for classification. We then examine the assumptions made by causal and non-causal feature selection methods when searching for the optimal feature set, and unify the assumptions by mapping them to the restrictions on the structure of the Bayesian network model of the studied problem. We further analyze in detail how the structural assumptions lead to the different levels of approximations employed by the methods in their search, which then result in the approximations in the feature sets found by the methods with respect to the optimal feature set. With the unified view, we are able to interpret the output of non-causal methods from a causal perspective and derive the error bounds of both types of methods. Finally, we present practical understanding of the relation between causal and non-causal methods using extensive experiments with synthetic data and various types of real-word data.

Kui Yu, Lin Liu, Jiuyong Li

In this paper, we study the problem of discovering the Markov blanket (MB) of a target variable from multiple interventional datasets. Datasets attained from interventional experiments contain richer causal information than passively observed data (observational data) for MB discovery. However, almost all existing MB discovery methods are designed for finding MBs from a single observational dataset. To identify MBs from multiple interventional datasets, we face two challenges: (1) unknown intervention variables; (2) nonidentical data distributions. To tackle the challenges, we theoretically analyze (a) under what conditions we can find the correct MB of a target variable, and (b) under what conditions we can identify the causes of the target variable via discovering its MB. Based on the theoretical analysis, we propose a new algorithm for discovering MBs from multiple interventional datasets, and present the conditions/assumptions which assure the correctness of the algorithm. To our knowledge, this work is the first to present the theoretical analyses about the conditions for MB discovery in multiple interventional datasets and the algorithm to find the MBs in relation to the conditions. Using benchmark Bayesian networks and real-world datasets, the experiments have validated the effectiveness and efficiency of the proposed algorithm in the paper.

Kui Yu, Xindong Wu, Wei Ding et al.

Feature selection is important in many big data applications. Two critical challenges closely associate with big data. Firstly, in many big data applications, the dimensionality is extremely high, in millions, and keeps growing. Secondly, big data applications call for highly scalable feature selection algorithms in an online manner such that each feature can be processed in a sequential scan. We present SAOLA, a Scalable and Accurate OnLine Approach for feature selection in this paper. With a theoretical analysis on bounds of the pairwise correlations between features, SAOLA employs novel pairwise comparison techniques and maintain a parsimonious model over time in an online manner. Furthermore, to deal with upcoming features that arrive by groups, we extend the SAOLA algorithm, and then propose a new group-SAOLA algorithm for online group feature selection. The group-SAOLA algorithm can online maintain a set of feature groups that is sparse at the levels of both groups and individual features simultaneously. An empirical study using a series of benchmark real data sets shows that our two algorithms, SAOLA and group-SAOLA, are scalable on data sets of extremely high dimensionality, and have superior performance over the state-of-the-art feature selection methods.